CLASS 10 MATHEMATICS
🎯 Ultimate Board Exam Formula Quick-Revision Guide 📚
📌 Real Numbers
• Euclid's Division Lemma: a = bq + r, where 0 ≤ r < b.
• Fundamental Theorem of Arithmetic: Every composite number can be uniquely expressed as a
product of primes.
HCF and LCM Relation
HCF(a, b) × LCM(a, b) = a × b
📌 Polynomials
Quadratic Polynomial Form: p(x) = ax² + bx + c
Relationship between Zeroes and Coefficients
Sum of Zeroes (α + β) = −b / a Product of Zeroes (α · β) = c / a
📌 Pair of Linear Equations in Two Variables
Ratio Comparison Graphical Behavior Algebraic Solution
a₁/a₂ ≠ b₁/b₂ Intersecting Lines Unique Solution
a₁/a₂ = b₁/b₂ = c₁/c₂ Coincident Lines Infinitely Solutions
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ Parallel Lines No Solution
📌 Quadratic Equations
Discriminant (D) & Roots Formula
D = b² − 4ac
x = [−b ± √D] / 2a
• If D > 0: Real & distinct roots | If D = 0: Real & equal roots | If D < 0: No real roots.
Created for Class 10 PSEB/CBSE Students | Good Luck! 🎓 Page 1 of 4
🎯 Ultimate Board Exam Formula Quick-Revision Guide 📚
📌 Real Numbers
• Euclid's Division Lemma: a = bq + r, where 0 ≤ r < b.
• Fundamental Theorem of Arithmetic: Every composite number can be uniquely expressed as a
product of primes.
HCF and LCM Relation
HCF(a, b) × LCM(a, b) = a × b
📌 Polynomials
Quadratic Polynomial Form: p(x) = ax² + bx + c
Relationship between Zeroes and Coefficients
Sum of Zeroes (α + β) = −b / a Product of Zeroes (α · β) = c / a
📌 Pair of Linear Equations in Two Variables
Ratio Comparison Graphical Behavior Algebraic Solution
a₁/a₂ ≠ b₁/b₂ Intersecting Lines Unique Solution
a₁/a₂ = b₁/b₂ = c₁/c₂ Coincident Lines Infinitely Solutions
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ Parallel Lines No Solution
📌 Quadratic Equations
Discriminant (D) & Roots Formula
D = b² − 4ac
x = [−b ± √D] / 2a
• If D > 0: Real & distinct roots | If D = 0: Real & equal roots | If D < 0: No real roots.
Created for Class 10 PSEB/CBSE Students | Good Luck! 🎓 Page 1 of 4
